Higher-dimensional subshifts of finite type, factor maps and measures of maximal entropy

Ronald Meester; Jeffrey E. Steif

doi:10.2140/pjm.2001.200.497

Higher-dimensional subshifts of finite type, factor maps and measures of maximal entropy

Pacific Journal of Mathematics ◽

10.2140/pjm.2001.200.497 ◽

2001 ◽

Vol 200 (2) ◽

pp. 497-510 ◽

Cited By ~ 10

Author(s):

Ronald Meester ◽

Jeffrey E. Steif

Keyword(s):

Finite Type ◽

Maximal Entropy ◽

Higher Dimensional ◽

Subshifts Of Finite Type ◽

Type Factor ◽

Factor Maps ◽

Measures Of Maximal Entropy

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Non-uniqueness of measures of maximal entropy for subshifts of finite type

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700007859 ◽

1994 ◽

Vol 14 (2) ◽

pp. 213-235 ◽

Cited By ~ 49

Author(s):

Robert Burton ◽

Jeffrey E. Steif

Keyword(s):

Finite Type ◽

Higher Dimensions ◽

One Dimension ◽

Maximal Entropy ◽

Subshift Of Finite Type ◽

Unique Measure ◽

Extremal Measures ◽

Subshifts Of Finite Type ◽

Measures Of Maximal Entropy ◽

Measure Of Maximal Entropy

AbstractIt is known that in one dimension an irreducible subshift of finite type has a unique measure of maximal entropy, the so-called Parry measure. Here we give a counterexample to this in higher dimensions. For this example, we also describe the geometric structure of the measures of maximal entropy and show that there are exactly two extremal measures.

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Measures that maximize weighted entropy for factor maps between subshifts of finite type

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385701001584 ◽

2001 ◽

Vol 21 (04) ◽

Cited By ~ 3

Author(s):

SUJIN SHIN

Keyword(s):

Finite Type ◽

Subshifts Of Finite Type ◽

Factor Maps ◽

Weighted Entropy

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A subshift of finite type that is equivalent to the Ising model

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700008518 ◽

1995 ◽

Vol 15 (3) ◽

pp. 543-556 ◽

Cited By ~ 4

Author(s):

Olle Häggström

Keyword(s):

Ising Model ◽

Finite Type ◽

Gibbs Measures ◽

Ergodic Measure ◽

Maximal Entropy ◽

Subshift Of Finite Type ◽

Translation Invariant ◽

Measures Of Maximal Entropy ◽

Natural Way ◽

Measure Of Maximal Entropy

AbstractFor the Ising model with rational parameters we show how to construct a subshift of finite type that is equivalent to this Ising model, in that the translation invariant Gibbs measures for the Ising model and the measures of maximal entropy for the subshift of finite type can be identified in a natural way. This is generalized to the non-translation invariant case as well. We also show how to construct, given any H > 0, an ergodic measure of maximal entropy for a subshift of finite type and a continuous factor, such that the factor has entropy H.

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